The validation set of a formula in a fuzzy logic is the set of all truth values which this formula may achieve. We summarize characterizations of validation sets of -fuzzy logics and extend them to the case of -fuzzy logics.
The main goal of this paper is to investigate very true MTL-algebras and prove the completeness of the very true MTL-logic. In this paper, the concept of very true operators on MTL-algebras is introduced and some related properties are investigated. Also, conditions for an MTL-algebra to be an MV-algebra and a Gödel algebra are given via this operator. Moreover, very true filters on very true MTL-algebras are studied. In particular, subdirectly irreducible very true MTL-algebras are characterized...